How do you find the product of #(2+v)^2#?

Question

1725 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-07T17:00:20

#v^2 + 4v + 4 #

First:

#(v+2)^2 = (v+2)(v+2) #

Now expand out using FOIL or another method you have been taught...

#( color(red)(v) + color(blue)(2) )(color(green)(v) +color(orange)(2) ) #

#=> color(red)(v) color(green)(v) + color(orange)(2) color(red)(v) + color(blue)(2)color(green)(v) + 2xx2 #

#=> v^2 + 4v + 4 #

Answer 2 · 2018-04-07T17:07:28

The product of #(2+v)^2# is #v^2+4v+4#.

The formula for squaring a binomial is as follows:
#(a+b)^2=a^2+2ab+b^2#

Thus,
#(2+v)^2#
#=2^2+2*2*v+v^2#
#=4+4v+v^2#
#=v^2+4v+4#